Synthesis of highly focused fields with circular polarization at any transverse plane

We develop a method for generating focused vector beams with circular polarization at any transverse plane. Based on the Richards-Wolf vector model, we derive analytical expressions to describe the propagation of these set of beams near the focal area. Since the polarization and the amplitude of the input beam are not uniform, an interferometric system capable of generating spatially-variant polarized beams has to be used. In particular, this wavefront is manipulated by means of spatial light modulators displaying computer generated holograms and subsequently focused using a high numerical aperture objective lens. Experimental results using a NA=0.85 system are provided: irradiance and Stokes images of the focused field at different planes near the focal plane are presented and compared with those obtained by numerical simulation.

Monotonic continuous-time random walks with drift and stochastic reset events

In this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonic continuous-time random walks with a constant drift: The process increases between the reset events, either by the effect of the random jumps, or by the action of the deterministic drift. As a result of all these combined factors interesting properties emerge, like the existence (for any drift strength) of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior. General formulas for two extreme statistics, the survival probability, and the mean exit time, are also derived. To corroborate in an independent way the results of the paper, Monte Carlo methods were used. These numerical estimations are in full agreement with the analytical predictions.

Prevalence of alcohol-impaired drivers based on random breath tests in a roadside survey

Sobriety checkpoints are not usually randomly located by traffic authorities. As such, information provided by non-random alcohol tests cannot be used to infer the characteristics of the general driving population. In this paper a case study is presented in which the prevalence of alcohol-impaired driving is estimated for the general population of drivers. A stratified probabilistic sample was designed to represent vehicles circulating in non-urban areas of Catalonia (Spain), a region characterized by its complex transportation network and dense traffic around the metropolis of Barcelona. Random breath alcohol concentration tests were performed during spring 2012 on 7,596 drivers. The estimated prevalence of alcohol-impaired drivers was 1.29 PER CENT, which is roughly a third of the rate obtained in non-random tests. Higher rates were found on weekends (1.90 PER CENT on Saturdays, 4.29 PER CENT on Sundays) and especially at night. The rate is higher for men (1.45 PER CENT) than for women (0.64 PER CENT) and the percentage of positive outcomes shows an increasing pattern with age. In vehicles with two occupants, the proportion of alcohol-impaired drivers is estimated at 2.62 PER CENT, but when the driver was alone the rate drops to 0.84 PER CENT, which might reflect the socialization of drinking habits. The results are compared with outcomes in previous surveys, showing a decreasing trend in the prevalence of alcohol-impaired drivers over time.

On the longitudinal component of paraxial fields

The analysis of paraxial Gaussian beams features in most undergraduate courses in laser physics, advanced optics and photonics. These beams provide a simple model of the field generated in the resonant cavities of lasers, thus constituting a basic element for understanding laser theory. Usually, uniformly polarized beams are considered in the analytical calculations, with the electric field vibrating at normal planes to the propagation direction. However, such paraxial fields do not verify the Maxwell equations. In this paper we discuss how to overcome this apparent contradiction and evaluate the longitudinal component that any paraxial Gaussian beam should exhibit. Despite the fact that the assumption of a purely transverse paraxial field is useful and accurate, the inclusion of the above issue in the program helps students to clarify the importance of the electromagnetic nature of light, thus providing a more complete understanding of the paraxial approach.

Transverse and longitudinal components of the propagating and evanescent waves associated to radially-polarized nonparaxial fields

A comparison is established between the contributions of transverse and longitudinal components of both the propagating and the evanescent waves associated to freely propagating radially polarized nonparaxial beams. Attention is focused on those fields that remain radially polarized upon propagation. In terms of the plane-wave angular spectrum of these fields, analytical expressions are given for determining both the spatial shape of the above components and their relative weight integrated over the whole transverse plane. The results are applied to two kinds of doughnut-like beams with radial polarization, and we compare the behavior of such fields at two transverse planes.

Persistent random walk model for transport trough thin slabs

We present a model for transport in multiply scattering media based on a three-dimensional generalization of the persistent random walk. The model assumes that photons move along directions that are parallel to the axes. Although this hypothesis is not realistic, it allows us to solve exactly the problem of multiple scattering propagation in a thin slab. Among other quantities, the transmission probability and the mean transmission time can be calculated exactly. Besides being completely solvable, the model could be used as a benchmark for approximation schemes to multiple light scattering.

Measuring school demand in the presence of spatial dependence. A conditional approach

Improving educational quality is an important public policy goal. However, its success requires identifying factors associated with student achievement. At the core of these proposals lies the principle that increased public school quality can make school system more efficient, resulting in correspondingly stronger performance by students. Nevertheless, the public educational system is not devoid of competition which arises, among other factors, through the efficiency of management and the geographical location of schools. Moreover, families in Spain appear to choose a school on the grounds of location. In this environment, the objective of this paper is to analyze whether geographical space has an impact on the relationship between the level of technical quality of public schools (measured by the efficiency score) and the school demand index. To do this, an empirical application is performed on a sample of 1,695 public schools in the region of Catalonia (Spain). This application shows the effects of spatial autocorrelation on the estimation of the parameters and how these problems are addressed through spatial econometrics models. The results confirm that space has a moderating effect on the relationship between efficiency and school demand, although only in urban municipalities.

Design of highly focused fields that remain unpolarized on axis

Research on the properties of highly focused fields mainly involved fully polarized light, whereas partially polarized waves received less attention. The aim of this Letter is to provide an appropriate framework, for designing some features of the focused field, when dealing with incoming partially polarized beams. In particular, in this Letter, we describe how to get an unpolarized field on the axis of a high numerical aperture objective lens. Some numerical results that corroborate theoretical predictions are provided.

LSB Matching Steganalysis Based on Patterns of Pixel Differences and Random Embedding

Peer-reviewed

Random walk radiosity with generalized absorption probabilities

The author studies random walk estimators for radiosity with generalized absorption probabilities. That is, a path will either die or survive on a patch according to an arbitrary probability. The estimators studied so far, the infinite path length estimator and finite path length one, can be considered as particular cases. Practical applications of the random walks with generalized probabilities are given. A necessary and sufficient condition for the existence of the variance is given, together with heuristics to be used in practical cases. The optimal probabilities are also found for the case when one is interested in the whole scene, and are equal to the reflectivities

Empirical welfare analysis: when preferences matter

Fleurbaey and Maniquet have proposed the criteria of conditional equality and of egalitarian equivalence to assess the equity among individuals in an ordinal setting. Empirical applications are rare and only partially consistent with their framework. We propose a new empirical approach that relies on individual preferences, is consistent with the ordinal criteria and enables to compare them with the cardinal criteria. We estimate a utility function that incorporates individual heterogeneous preferences, obtain ordinal measures of well-being and apply conditional equality and egalitarian equivalence. We then propose two cardinal measures of well-being, that are comparable with the ordinal model, to compute Roemer’s and Van de gaer’s criteria. Finally we compare the characteristics of the worst-off displayed by each criterion. We apply this model to a sample of US micro data and obtain that about 18% of the worst-off are not common to all criteria.